The U’s secured promotion into the Championship from League One last season and are now preparing for a campaign in the second tier.
Brannagan, 28, was a key man in helping Oxford to win promotion, making 46 appearances across their regular League One campaign and the playoffs.
He is though entering the final year of his contract at the club and sides are spying an opportunity.
Two Championship clubs, in the shape of Blackburn and West Brom, are keen on the midfielder.
Both are plotting to make an approach to test Oxford for Brannagan.
Leaving Oxford could be a wrench for Brannagan, with the midfielder joining the club from boyhood side Liverpool in 2018.
He has made close to 300 appearances in an Oxford shirt and may want to help the side in the Championship next term.
However, Blackburn and West Brom could present tempting destinations for the midfielder.
